{"paper":{"title":"Kernelized Advantage Estimation: From Nonparametric Statistics to LLM Reasoning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Applying kernel smoothing to a small number of reasoning traces yields accurate value and gradient estimates that improve policy optimization in LLM reasoning.","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Chengchun Shi, Hongyi Zhou, Jin Zhu, Kai Ye, Shijin Gong, Xinyu Zhang","submitted_at":"2026-04-30T15:27:34Z","abstract_excerpt":"Recent advances in large language models (LLMs) have increasingly relied on reinforcement learning (RL) to improve their reasoning capabilities. Three types of approaches have been widely adopted: The first relies on a deep neural network to estimate the value function of the learning policy in order to reduce the variance of the policy gradient. However, estimating and maintaining such a value network incurs substantial computational and memory overhead. The second avoids training a value network by approximating the value function using sample averages. However, it samples a large number of "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Numerical and theoretical results demonstrate that our proposal achieves accurate value and gradient estimation, leading to improved policy optimization.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Kernel smoothing applied to a small number of reasoning traces per prompt can produce sufficiently unbiased and low-variance estimates of the true value function in the high-dimensional, discrete space of LLM outputs.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Kernel smoothing yields accurate value and gradient estimates for low-variance policy learning in LLM reasoning under tight per-prompt sampling budgets.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Applying kernel smoothing to a small number of reasoning traces yields accurate value and gradient estimates that improve policy optimization in LLM reasoning.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4e51d9dc8e7157fb6d02d3fd657553107212253a70ec9ad1e66d75340fe6546f"},"source":{"id":"2604.28005","kind":"arxiv","version":2},"verdict":{"id":"7ea2283d-b225-4cef-aacf-67b8e11dc751","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T06:54:54.394441Z","strongest_claim":"Numerical and theoretical results demonstrate that our proposal achieves accurate value and gradient estimation, leading to improved policy optimization.","one_line_summary":"Kernel smoothing yields accurate value and gradient estimates for low-variance policy learning in LLM reasoning under tight per-prompt sampling budgets.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Kernel smoothing applied to a small number of reasoning traces per prompt can produce sufficiently unbiased and low-variance estimates of the true value function in the high-dimensional, discrete space of LLM outputs.","pith_extraction_headline":"Applying kernel smoothing to a small number of reasoning traces yields accurate value and gradient estimates that improve policy optimization in LLM reasoning."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.28005/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T18:41:39.195940Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"502ab46ad05790b13427aaf41050b2578545341505d347dddf670c30aa51c5cb"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}